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This dictionary is intended for use primarily by speakers of English who need to understand Russian mathematical writing and/or to translate such writing. As far as possible, the "definitions" are translations rather than explanations, and reflect current usage in mathematical writing. The vocabulary has been extensively enlarged and brought up to date, although it retains some obsolete terms that may be needed by users who have to consult older literature. Users may encounter material that has not been composed in the most approved or correct style. Therefore, some words that are frowned on by Soviet purists have been retained, or added, because they occur in writing by Soviet authors whose native language is not Russian, and whose knowledge of Russian is less than perfect. The dictionary must not be inverted: that is, read backwards as an English-Russian dictionary. We have attempted to give idiomatic translations, but a Russian word is not necessarily a correct or exact equivalent of the English word that is used to translate it in a particular context. Just because краевая задача can be correctly translated as "boundary value problem" does not mean that either, or any part, of the Russian words means "value."